If you want to get a feel of the mechanics, I recommend Gilbert Strang’s Linear Algebra over Khan Academy and Brilliant.
I think part of the 3b1b series is based on that book and they have similar structures. Just sit down for 1-2 hours with some graph papers + mechanical pencil and do the end-of-chapter exercises, they are designed to reinforce the concepts.
In my experience, thinking hard doesn’t hurt my head directly. However, trying to think hard under stress and sleep loss does. Whenever I noticed my head hurts trying to “think hard”, it’s usually a symptom that something else is going wrong.